(* Title: HOL/Hyperreal/hypreal_arith.ML
ID: $Id$
Author: Tobias Nipkow, TU Muenchen
Copyright 1999 TU Muenchen
Simprocs for common factor cancellation & Rational coefficient handling
Instantiation of the generic linear arithmetic package for type hypreal.
*)
local
val simps = [thm "star_of_zero",
thm "star_of_one",
thm "star_of_number_of",
thm "star_of_add",
thm "star_of_minus",
thm "star_of_diff",
thm "star_of_mult"]
val real_inj_thms = [thm "star_of_le" RS iffD2,
thm "star_of_less" RS iffD2,
thm "star_of_eq" RS iffD2]
in
val hyprealT = Type ("StarDef.star", [HOLogic.realT]);
val fast_hypreal_arith_simproc =
Simplifier.simproc (the_context ())
"fast_hypreal_arith"
["(m::hypreal) < n", "(m::hypreal) <= n", "(m::hypreal) = n"]
Fast_Arith.lin_arith_prover;
val hypreal_arith_setup =
Fast_Arith.map_data (fn {add_mono_thms, mult_mono_thms, inj_thms, lessD, neqE, simpset} =>
{add_mono_thms = add_mono_thms,
mult_mono_thms = mult_mono_thms,
inj_thms = real_inj_thms @ inj_thms,
lessD = lessD, (*Can't change LA_Data_Ref.lessD: the hypreals are dense!*)
neqE = neqE,
simpset = simpset addsimps simps}) #>
arith_inj_const ("StarDef.star_of", HOLogic.realT --> hyprealT) #>
(fn thy => (change_simpset_of thy (fn ss => ss addsimprocs [fast_hypreal_arith_simproc]); thy));
end;